Many firms undertake direct marketing campaigns to promote their products. The campaigns typically involve mailing information to millions of households. The response rates are carefully monitored to determine the demographic characteristics of respondents. By studying tendencies to respond, the firms can better target future mailings to those segments of the population most likely to purchase their products.

Suppose a distributor of mail-order tools is analyzing the results of a recent mailing. The probability of response is believed to be related to income and age. The percentages of the total number of respondents to the mailing are given by income and age classification in Table 3.4. This table is called a two-way table because responses are classified according to two variables, income (columns) and age (rows).

Define the following events:

a. Find P(A) and P(B). 

b. Find P(A ⋃ B).

c. Find P(A ⋂ B).

Data from Table 3.4

Transcribed Image Text:

respondent's A: [A B: (A respondent's income is more than $50,000.} age is 30 or more.}